Dip chicken in the flour to lightly coat both sides. In a large skillet over medium-high heat, melt butter with oil. Add the chicken and saute for about 2 minutes. Turn and add the sliced mushrooms to the skillet. Continue cooking for about 2 minutes longer, stirring mushrooms occasionally.

Add the Marsala wine, chicken broth, and lemon and bring to a simmer. Simmer, uncovered, for 5 minutes to reduce slightly. Cover and continue cooking for 5 minutes longer. Add the basil, cream, and green onions and cook for 2 minutes longer.